Some evolving network models only consider the addition of nodes [1]}, although some works consider deletion of nodes during/beyond the evolution of the networks [2]}, [3]}, [4]}. There are only a few networks such as citation, movie actor collaboration and science collaboration networks which can be described without removal of links. But other real-world networks, e.g., like the Internet, communication networks, WWW, transportation networks have the varying composition of links due to appearance or disappearance of connections. A link may disappear due to break down and sometimes removed forcibly to balance the traffic loads in the communication networks. Few heavily loaded nodes get the opportunity to rewire (remove a connection from a node and attach with another node) their links. In this context, the proposed work considers designing of a TVCN model, minimization of network congestion and a fair sharing of resources among the users according to their willingness to pay. A TVCN is designed where nodes, as well as links, are getting added into the networks while restructuring is performed in the existing networks through rewiring and removal of the links. Addition and rewiring of links are based on preferential attachment while removal of links is based on anti-preferential attachment [5]}. Probability \( \Pi _i \)  that a node \( i \)  will be selected through preferential attachment is proportional to its in-degree and is given by, \( \frac{k_i}{\sum _{j \in N} k_j} \)  where, \( k_i \)  is in-degree and the probability \( \Pi ^{\prime }_i \)  of selecting node \( i \)  with anti-preferential attachment is given by, \( \frac{1}{|N|-1} \left(1-\frac{k_i}{\sum _{j \in N} k_j}\right) \) . Rewiring of links is done to redistribute the traffic loads, while few links increase the maintenance cost so these links may be chosen for removal from the network. After designing the network, users select their routes for data communication with their destination nodes. Optimality of the routes is checked by using the proposed window-based congestion control scheme at different time intervals.
